>>>>>>>On the 1st day of Xmas, my true love gave to me:
>>>>>>>1 item
>>>>>>>On the 2nd day of Xmas, my true love gave to me:
>>>>>>>2 items + 1 item
>>>>>>>On the 3rd day of Xmas, my true love gave to me:
>>>>>>>3 items + 2 items + 1 item
>>>>>>>.
>>>>>>>.
>>>>>>>On the n-1 day of Xmas, my true love gave to me:
>>>>>>>n-1 items + n-2 items + ... + 1 item
>>>>>>>On the nth day of Xmas, my true love gave to me:
>>>>>>>n items + n-1 items + ... + 1 item
>>>>>>>
>>>>>>>How many total items did my true love give to me, as a function of n?
>>>>>>
>>>>>>Number of gifts = gifts(n)
>>>>>>
>>>>>>
>>>>>>FUNCTION gifts(n)
>>>>>>lnReturn = 0
>>>>>>FOR I = 1 TO n
>>>>>> FOR H = 1 TO I
>>>>>> lnReturn = lnReturn + H
>>>>>> ENDFOR
>>>>>>ENDFOR
>>>>>>RETURN lnReturn
>>>>>>
>>>>>>
>>>>>>not arithmetic, but it works
>>>>>
>>>>>Er, yes, but there is an elegant mathematical solution that even a computer would like! (no looping involved)
>>>>
>>>>
>>>>Maybe it can be : Gifts = (n+1) * (n/2) ??
>>>
>>>Um, no, we've seen that one earlier...that's not the cumulative sum for all the days, that's only one day...
>>
>>Sum=(N^3)/6+(N^2)/2+N/3
>>If this is right, I will send you bill ::)
>
>I guess this is pretty much the same thing, but this is what I came up with:
>(N*(N+2)/3)*(N+1)/2

For N=12;&&Number of days of christmas
sum = 364

True love should have just given one gift a day on every day of the year except christmas day, and saved all the trouble.